In filter bank multi carrier (FBMC) transmission, the transmitted signal is given by
                                          s            ⁡                          (              t              )                                =                                    ∑                              n                =                0                                            N                -                1                                      ⁢                                                  ⁢                                          ∑                                  k                  =                  0                                                  K                  -                  1                                            ⁢                                                d                                      k                    ,                    n                                                  ⁢                                  j                                                                                    (                                                  k                          +                          n                                                )                                            ⁢                      π                                        2                                                  ⁢                                  g                  ⁡                                      (                                          t                      -                                              nT                        2                                                              )                                                  ⁢                                  e                                                            j                      ⁢                      2                                        ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                    kFt                                                                                      ,                            (        1        )            where the prototype filter g(t) is the information carrying pulse (or Nyquist pulse), dk,n are real data symbols, K is the number of subcarriers, N is the number of pulses per transmitted FBMC symbol duration, and t=0, 1, . . . , KN−1. The prototype filter, which may be chosen real and symmetric, is at the focus of design efforts. For instance, side lobes of a purposefully designed FBMC prototype filter may be significantly smaller than those in orthogonal frequency division multiplexing (OFDM), and FBMC may allow for transmitting signals with a spectrum that can be pre-specified within wide bounds.
FBMC modulation may be superior to cyclically prefixed (CP) OFDM as regards one or more of flexibility, spectral efficiency and spectral containment, both in wired and wireless applications. FBMC/OQAM or OFDM/OQAM, where offset quadrature amplitude modulation (OQAM) is employed, has attracted recent interest. Kofidis et al., “Preamble-based channel estimation in OFDM/OQAM systems: A review”, Signal Processing, vol. 93 (2013), pp. 2038-2054, discusses the channel estimation problem for such systems.
Channel estimation may be based on known symbols (or pilot symbols) transmitted at known frequency-time (FT) positions of a signal. A block containing one or more pilot symbols may be referred to as a preamble or midamble depending on its position in a frame-segmented signal; so-called scattered pilot symbols are located at isolated FT positions. By comparing received pilot symbols (as decoded from their known positions) and comparing them with their known values, a receiving side may gain knowledge of current channel characteristics. While the pilot symbols represent overhead in a communication system, it can be shown that their number is bounded below as a function of the modulation scheme and current radio conditions.
A difficulty associated with channel estimation in the FBMC/OQAM setting is related to the fact that, while the subcarrier functions are orthogonal in the real field, there is an intrinsic imaginary interference among subcarriers and symbols. Kofidis et al. reviews known approaches to this difficulty, including a direct approach for low-noise conditions (“pairs-of-pilots” method), interference avoidance (by nulling data surrounding the pilot symbols) and interference approximation (by pairwise approximate cancellation of interference terms). Interference approximation is based on an assumption of approximate constancy of the channel and further on knowledge regarding interference weights for the neighbors of each FT point of interest; Kofidis et al. attempts to prove symmetry relations applying between the interference weights. In the interference approximation method, some neighboring symbols are repeated (with same or different phase) in view of the symmetry relations, and so cannot be used for data transmission without constraints. It would be desirable to reduce the system overhead devoted to channel estimation.